What is (x^2y^2-9)/(3-xy) ?

The solution to (x^2y^2-9)/(3-xy) is -xy-3

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simplify (x^2y^2-9)/(3-xy)

simplify

\frac{x ^{2} y ^{2} - 9}{3 - x y}

- x y - 3

Solution steps

\frac{x ^{2} y ^{2} - 9}{3 - x y}

Factor

x^{2} y^{2} - 9 : (x y + 3) (x y - 3)

= \frac{( x y + 3 ) ( x y - 3 )}{3 - x y}

3 - x y = - (x y - 3)

= \frac{( x y + 3 ) ( x y - 3 )}{- ( x y - 3 )}

Cancel the common factor:

x y - 3

= \frac{x y + 3}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (x y + 3)

Apply the distributive law:

- (a + b) = - a - b

- (x y + 3) = - x y - 3

= - x y - 3

\frac{x ^{2} + 2 x - 8}{x ^{2} - 16}

\frac{t ^{2} - 5 t + 6}{t ^{2} - t - 2}

x^{2} + x - 110

- a

2 y